1. **State the problem:** Peter brings jars of honey and honeycombs to the market in a ratio of 10 jars to 3 honeycombs. We need to find which pairs of jars and honeycombs maintain this equivalent ratio. 2. **Formula and rule:** Two ratios $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent if $a \times d = b \times c$. 3. **Check each option:** - Option A: $\frac{18}{5}$ Calculate cross products: $18 \times 3 = 54$, $10 \times 5 = 50$; since $54 \neq 50$, not equivalent. - Option B: $\frac{20}{6}$ Calculate cross products: $20 \times 3 = 60$, $10 \times 6 = 60$; since $60 = 60$, equivalent. - Option C: $\frac{30}{9}$ Calculate cross products: $30 \times 3 = 90$, $10 \times 9 = 90$; since $90 = 90$, equivalent. - Option D: $\frac{40}{10}$ Calculate cross products: $40 \times 3 = 120$, $10 \times 10 = 100$; since $120 \neq 100$, not equivalent. 4. **Answer:** The pairs that maintain the equivalent ratio are options B and C. **Final answer:** B and C